The Use of Cubic Splines and MATLAB for the Determination of BOD First-Order Model Coefficients

Abstract

The purpose of this paper is to introduce a new method for the determination of the values of the first-order Biochemical Oxygen Demand (BOD) model coefficients (k and L).Cubic spline interpolation and MATLAB were used for that purpose after the experimental and theoretical BOD values were made dimensionless. Experimental BOD values taken from the literature are made dimensionless by dividing them by experimental BOD1 through BOD5. Theoretical BOD values are made dimensionless by dividing them by the theoretical BOD1 through BOD5 for different theoretical k values. Experimental dimensionless BOD values are connected smoothly using cubic spline method. Using MATLAB, the closest theoretical dimensionless BOD curve to the cubic spline curve is selected and used for the determination of k and L. The closest curve is the one that has the same area under it as to that under the cubic spline curve with the areas that lie between the two curves being the smallest. The new method has proved to give more accurate values after it has been compared with a number of other methods used for that purpose.The new method produced the smallest error and the highest coefficient of determination than the other methods used. The newly introduced method is expected to replace all other methods, as these methods give different values for k and L depending on the method used.